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Solution of nonlinear degenerate elliptic-parabolic systems in Orlicz- Sobolev spaces. (English) Zbl 0722.35048
Differential equations and their applications, Proc. 7th Conf., Equadiff 7, Prague/Czech. 1989, Teubner-Texte Math. 118, 175-179 (1990).
[For the entire collection see Zbl 0704.00019.]
A double nonlinear parabolic system of the form \[ \partial_ tb(u)- \nabla a(t,x,\nabla u)=f(t,x,b(u)) \] with a mixed (Dirichlet-Neumann) nonlinear boundary condition is considered where b is a gradient of \(C^ 1\)-convex function and a is monotone and coercive in \(\nabla u\). An existence of a variational solution is proved, generally, in nonreflexive functional spaces of Orlicz-Sobolev type.
Reviewer: J.Kačur

MSC:
35K60 Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations
35M10 PDEs of mixed type
35D05 Existence of generalized solutions of PDE (MSC2000)
Citations:
Zbl 0704.00019